Question

Solve the simultaneous equation 4x^2 - 9y^2 = 19

Answer 1

The line 2x +3y = 1 is tangent to 4x^2 -9y^2 = 19

:

Solve the linear equation for y

:

1) y = -2x/3 +1/3

:

substitute for y in the equation of the hyperbole

:

4x^2 -9(-2x/3 +1/3)^2 = 19

:

4x^2 -9(4x^2/9 -4x/9 +1/9) = 19

:

4x^2 -4x^2 +4x -1 = 19

:

4x -20 = 0

:

4x = 20

:

x = 5

:

use equation 1 to get the value of y

:

y = -2(5)/3 +1/3 = -3

:

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solution is x = 5, y = -3 which is the point (5, -3)

:

check the solution

:

hyperbole

:

4(5^2) -9(-3)^2 = 19

:

100 -81 = 19

:

19 = 19

:

Line

:

2(5) +3(-3) = 1

:

10 -9 = 1

:

1 = 1

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